1*05a0b428SJohn Marino /* @(#)k_sin.c 5.1 93/09/24 */
2*05a0b428SJohn Marino /*
3*05a0b428SJohn Marino * ====================================================
4*05a0b428SJohn Marino * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5*05a0b428SJohn Marino *
6*05a0b428SJohn Marino * Developed at SunPro, a Sun Microsystems, Inc. business.
7*05a0b428SJohn Marino * Permission to use, copy, modify, and distribute this
8*05a0b428SJohn Marino * software is freely granted, provided that this notice
9*05a0b428SJohn Marino * is preserved.
10*05a0b428SJohn Marino * ====================================================
11*05a0b428SJohn Marino */
12*05a0b428SJohn Marino
13*05a0b428SJohn Marino /* __kernel_sin( x, y, iy)
14*05a0b428SJohn Marino * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854
15*05a0b428SJohn Marino * Input x is assumed to be bounded by ~pi/4 in magnitude.
16*05a0b428SJohn Marino * Input y is the tail of x.
17*05a0b428SJohn Marino * Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
18*05a0b428SJohn Marino *
19*05a0b428SJohn Marino * Algorithm
20*05a0b428SJohn Marino * 1. Since sin(-x) = -sin(x), we need only to consider positive x.
21*05a0b428SJohn Marino * 2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0.
22*05a0b428SJohn Marino * 3. sin(x) is approximated by a polynomial of degree 13 on
23*05a0b428SJohn Marino * [0,pi/4]
24*05a0b428SJohn Marino * 3 13
25*05a0b428SJohn Marino * sin(x) ~ x + S1*x + ... + S6*x
26*05a0b428SJohn Marino * where
27*05a0b428SJohn Marino *
28*05a0b428SJohn Marino * |sin(x) 2 4 6 8 10 12 | -58
29*05a0b428SJohn Marino * |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2
30*05a0b428SJohn Marino * | x |
31*05a0b428SJohn Marino *
32*05a0b428SJohn Marino * 4. sin(x+y) = sin(x) + sin'(x')*y
33*05a0b428SJohn Marino * ~ sin(x) + (1-x*x/2)*y
34*05a0b428SJohn Marino * For better accuracy, let
35*05a0b428SJohn Marino * 3 2 2 2 2
36*05a0b428SJohn Marino * r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
37*05a0b428SJohn Marino * then 3 2
38*05a0b428SJohn Marino * sin(x) = x + (S1*x + (x *(r-y/2)+y))
39*05a0b428SJohn Marino */
40*05a0b428SJohn Marino
41*05a0b428SJohn Marino #include "math.h"
42*05a0b428SJohn Marino #include "math_private.h"
43*05a0b428SJohn Marino
44*05a0b428SJohn Marino static const double
45*05a0b428SJohn Marino half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
46*05a0b428SJohn Marino S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */
47*05a0b428SJohn Marino S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */
48*05a0b428SJohn Marino S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */
49*05a0b428SJohn Marino S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */
50*05a0b428SJohn Marino S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */
51*05a0b428SJohn Marino S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */
52*05a0b428SJohn Marino
53*05a0b428SJohn Marino double
__kernel_sin(double x,double y,int iy)54*05a0b428SJohn Marino __kernel_sin(double x, double y, int iy)
55*05a0b428SJohn Marino {
56*05a0b428SJohn Marino double z,r,v;
57*05a0b428SJohn Marino int32_t ix;
58*05a0b428SJohn Marino GET_HIGH_WORD(ix,x);
59*05a0b428SJohn Marino ix &= 0x7fffffff; /* high word of x */
60*05a0b428SJohn Marino if(ix<0x3e400000) /* |x| < 2**-27 */
61*05a0b428SJohn Marino {if((int)x==0) return x;} /* generate inexact */
62*05a0b428SJohn Marino z = x*x;
63*05a0b428SJohn Marino v = z*x;
64*05a0b428SJohn Marino r = S2+z*(S3+z*(S4+z*(S5+z*S6)));
65*05a0b428SJohn Marino if(iy==0) return x+v*(S1+z*r);
66*05a0b428SJohn Marino else return x-((z*(half*y-v*r)-y)-v*S1);
67*05a0b428SJohn Marino }
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